1. Field of the Invention
This invention relates to the mechanical arts. In particular, it relates to instruments for measuring the flow of fluids, such as gases.
2. Discussion of Relevant Art
The control of the mass flow of gases is important in many industries. During the manufacture of semiconductors, for example, many of the processes require a precise reaction of two or more gases under carefully controlled conditions. Since chemical reactions occur on a molecular level, the control of mass flow is the most direct way to regulate the gases.
Not only is it important that the amount of gas be precisely controlled, but it is important that the gas be free from contamination. In the manufacture of semiconductor devices having features the size of only one micron or less, the presence of any foreign contaminants in the gas stream is extremely undesirable. Particles, vapors and contaminant gases, such as dust, metal, lint, moisture, solvents, oil, air or other process gases can cause spoilage of the products. It is therefore important that the flow splitters used in mass flow meters neither trap such contaminants and subsequently release them to the gas stream, nor generate such contaminants during normal calibration and operation.
There have been developed in the art a variety of instruments for measuring the mass flow rate of gases from below 5 standard cubic centimeters per minute (SCCM) to more than 500,000 SCCM. The prevalent design of such instruments requires that the flow of the gas be divided into two or more paths.
In a typical instrument, a small flow is routed through a sensor assembly where the mass flow is measured, while most of the flow is routed through a flow splitter section located in parallel with the sensor assembly. The sensor assembly contains a capillary tube two with resistance thermometers wound on the outside. The resistance thermometers form two legs of an electronic bridge; the other two legs are usually fixed resistors. The bridge is carefully designed and manufactured such that the two resistors are as identical as possible in electrical and mechanical characteristics. When a voltage is applied across the bridge, current moves through each resistance thermometer causing them to self-heat. When there is no flow of gas through the capillary tube, both of the thermometers heat up identically. As gas begins to flow through the tube, the gas cools the first resistance thermometer and transfers a portion of that heat to the second one, causing it to get warmer. The temperature difference between the two thermometers is a function of mass flow.
Flow through a gap or conduit can be characterized by a non-dimensional parameter known as the Reynold's number. The meaning of Reynold's number is well known in the art and a discussion is found, inter alia, in U.S. Pat. No. 4,524,616, which patent is incorporated herein by reference. The Reynold's number for flow through a conduit can be determined using the formula: EQU R=4 mPV.sub.m /.mu.
where P is the density of the fluid, V.sub.m is the mean velocity of the conduit, .mu. is the fluid viscosity and m is the hydraulic radius defined as the conduit area divided by the wetted perimeter of the conduit. The effective diameter of the conduit can be considered to be 4 m.
The Reynold's number expresses the ratio of the inertial forces to the viscous forces in the fluid. For low values of R, the flow is laminar, while for high values of R, inertial forces predominate and the flow tends to be turbulent. The Reynold's number corresponding to the transition between laminar and turbulent flow generally occurs in the range of about 1,600 to about 2,800; i.e., a Reynold's number of less than 1,600 may be assumed to enable laminar flow.
The geometry of the capillary tubes used in the sensor assemblies of flow meters is chosen to constrain flow of the fluid to the laminar region, that is, to a Reynold's number less than about 1,600. Under laminar flow conditions in the capillary tube, ignoring the effects of secondary kinetic losses and the effects of heat addition from the resistance thermometers, mass flow will be linear with respect to the pressure drop across the capillary tube.
Linearity is a desired quality in mass flow measurement and control. A linear mass flow system greatly simplifies interaction with an instrument's automatic process control systems. In addition, the ability to use a flowmeter on gases different than the gas initially used for calibration enables the user to switch from gas to gas without recalibration, and allows the user to employ a non-hazardous gas to calibrate flowmeters ultimately used on hazardous gases.
Assuming a perfectly linear mass flow sensor assembly using a capillary tube, to obtain a perfectly linear flow measurement, the capillary tube and the flow splitter section should have identical flow characteristics. If they do, the ratio between the flow through the capillary tube and the flow through the flow splitter section remains constant for different gases, temperatures, pressures and mass flow rates. As a result of this constant ratio, total flow can be determined from the measurement of the partial flow through the capillary tube.
If the ratio varies due to differences between the flow characteristics of the two paths, the sensor assembly signal must be electronically modified to compensate for the varying split ratio and to linearize its output with the total flow through, and possibly the temperature of the gas in, the flow meter section. Knowing and making modifications for a varying split ratio, although possible, complicates the measuring task and introduces varying degrees of inaccuracy due to unit to unit manufacturing variation. If the ratio varies with flow rate, the flow through the sensor assembly will not be a true measure of the total flow. The amount of error, when there is not a constant split flow ratio, increases as the ratio becomes more dependent on the flow rate.
A constant ratio can be achieved by creating conditions in which the mass flow rate through the fluid path and the sensor assembly are a linear function of the pressure drop across the fluid inlet and outlet. Given these conditions, the ratio becomes independent of the mass flow rate. Calculation of the total flow can then be accurately calculated from the measurement of the flow through the sensor assembly over the entire flow range using the formulae: ##EQU1## where: R=the ratio, k.sub.B1 =the linear flow restriction coefficient due to the geometry of the fluid path, k.sub.s1 =the linear flow restriction coefficient due to the geometry of the sensor, .DELTA.P=the pressure drop, m.sub.b =the mass flow rate through the fluid path and m.sub.s =the mass flow rate through the sensor.
If the mass flow through the fluid path is not linear with pressure drop, the ratio no longer simplifies as illustrated above. The gas passing through the fluid path increases in velocity at the expense of pressure as the cross sectional area of the fluid path is reduced. Therefore, it is a desideratum that, with the exception of linear viscous losses, all the energy contained in the gas velocity, a non-linear quantity, is converted back into pressure by the time the gas exits the fluid path. The portion that is not recovered is called a kinetic loss and causes the pressure drop across the fluid path to be non-linear with flow. The ratio then takes the form: ##EQU2## where: k.sub.B1 =the fluid path's linear flow restriction coefficient, k.sub.s1 =the sensor's linear flow restriction coefficient, k.sub.B2 =the fluid path's non-linear flow restriction coefficient, k.sub.s2 =the sensor's non-linear flow restriction coefficient, and .DELTA.P=the pressure drop. Since .DELTA.P varies with flow, the ratio is not constant and, therefore, the sensor assembly output requires electronic modification.
Flow geometries through the sensor assembly and the fluid path are designed to reduce the effects of the non-linear terms on the ratio by constraining the flow conditions to the laminar region. However, disturbing the laminar flow profile of such designs will still create non-linear kinetic losses. Typical disturbances in the laminar flow profile can be caused by sudden contractions and expansions in the fluid path, such as by fluid entrance and exit transitions; by pressure increases due to rapid deceleration of the gas stream in an expanding cross section causing the localized back-flowing of gases; and by momentum changes due to sharp and/or repeated changes in the direction of the fluid flow.
U.S. Pat. No. 3,851,526 discloses a flowmeter in which a laminar flow conduit is connected in parallel to a flow splitter which has a series of disks with radial slots etched into one face. The slots have dimensions such that the gas flow is laminar. However, when these disks are stacked together and held in the flow path with a mounting nut, gas enters the nut, flows first radially outward, then axially, then radially inward and finally, flows axially again. Consequently, this design forces the gas to make four 90 degree turns. A momentum change is associated with each turn. Moreover, there is a sudden expansion as the gas exits the disks. Both factors cause kinetic losses which create non-linearity. The faying surfaces of the disks also trap contaminants (including moisture), so that purging is difficult. Another problem with this design is that the pressure drop depends on the torque of the nut and can be different each time the flow splitter is disassembled and reassembled.
U.S. Pat. No. 3,792,609 discloses a flow splitter which has an orifice followed by a series of closely-packed fine screens. This design also suffers from momentum losses as the gas zigzags its way through the screens.
U.S. Pat. No. 4,524,616 discloses a combination bypass and sensor in which the flow splitting function is accomplished within the flow splitter section itself. It consists of a tapered flow splitter adjustably secured in a tapered bore in the flowmeter housing, so as to form an annular fluid path. Two boreholes are drilled through the housing to operationally connect the sensor to the bore. The device is adjusted by moving the flow splitter in and out on a threaded shaft. Such an adjusting mechanism contains dead spaces in its threads and shaft, which make purging difficult.
In the preferred embodiment of the device disclosed in U.S. Pat. No. 4,524,616, the boreholes are both connected to the annular region formed between the bore and the flow splitter. This embodiment is expensive to manufacture. Because of the location of the boreholes, the pressure drop through the sensor is very sensitive to the concentricity of the flow splitter in the bore, thus the flow splitter must be concentric with the bore within extremely close tolerances.
In the non-preferred embodiment of the device where the two boreholes are located on each side of the annular flow path, there occurs high kinetic losses due to the rapid reduction of static pressure, as the gas enters the annular fluid path, and rapid increase of the static pressure, as it exits. In the non-preferred embodiment where one borehole is located outside the annular flow area and the other borehole is located inside the laminar flow area, there results a non-linear manometer effect due to the markedly different gas velocities at the boreholes.
Now, there has been found a flowmeter which overcomes these disadvantages. The flowmeter in accordance with the invention includes a flow splitter section which provides excellent linearity over a wide range of flow rates for a great variety of gases. This means, for example, that the flowmeter can be calibrated with a non-toxic gas and then the performance of a toxic gas accurately computed.
The simple design of the flow splitter section in accordance with the invention can be manufactured relatively inexpensively out of stainless steel without forming any significant cracks, crevices, or faying surfaces and without any plastic or elastomeric parts. The fluid path contains a minimum amount of dead space or threads which could trap gases. Therefore, problems with contamination and difficulties in purging are minimized.